Dual spaces of local Morrey-type spaces

Amiran Gogatishvili; Rza Mustafayev

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 3, page 609-622
  • ISSN: 0011-4642

Abstract

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In this paper we show that associated spaces and dual spaces of the local Morrey-type spaces are so called complementary local Morrey-type spaces. Our method is based on an application of multidimensional reverse Hardy inequalities.

How to cite

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Gogatishvili, Amiran, and Mustafayev, Rza. "Dual spaces of local Morrey-type spaces." Czechoslovak Mathematical Journal 61.3 (2011): 609-622. <http://eudml.org/doc/196497>.

@article{Gogatishvili2011,
abstract = {In this paper we show that associated spaces and dual spaces of the local Morrey-type spaces are so called complementary local Morrey-type spaces. Our method is based on an application of multidimensional reverse Hardy inequalities.},
author = {Gogatishvili, Amiran, Mustafayev, Rza},
journal = {Czechoslovak Mathematical Journal},
keywords = {local Morrey-type spaces; complementary local Morrey-type spaces; associated spaces; dual spaces; multidimensional reverse Hardy inequalities; local Morrey-type space; complementary local Morrey-type space; associated space; dual space},
language = {eng},
number = {3},
pages = {609-622},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Dual spaces of local Morrey-type spaces},
url = {http://eudml.org/doc/196497},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Gogatishvili, Amiran
AU - Mustafayev, Rza
TI - Dual spaces of local Morrey-type spaces
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 3
SP - 609
EP - 622
AB - In this paper we show that associated spaces and dual spaces of the local Morrey-type spaces are so called complementary local Morrey-type spaces. Our method is based on an application of multidimensional reverse Hardy inequalities.
LA - eng
KW - local Morrey-type spaces; complementary local Morrey-type spaces; associated spaces; dual spaces; multidimensional reverse Hardy inequalities; local Morrey-type space; complementary local Morrey-type space; associated space; dual space
UR - http://eudml.org/doc/196497
ER -

References

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  1. Burenkov, V. I., Guliyev, H. V., 10.4064/sm163-2-4, Stud. Math. 163 (2004), 157-176. (2004) MR2047377DOI10.4064/sm163-2-4
  2. Burenkov, V. I., Guliyev, H. V., Guliyev, V. S., On boundedness of the fractional maximal operator from complementary Morrey-type spaces to Morrey-type spaces, The Interaction of Analysis and Geometry. International School-Conference on Analysis and Geometry, Novosibirsk, Russia, August 23--September 3, 2004 American Mathematical Society (AMS) Providence Contemporary Mathematics 424 (2007), 17-32. (2007) MR2316329
  3. Burenkov, V. I., Guliyev, H. V., Guliyev, V. S., 10.1016/j.cam.2006.10.085, J. Comput. Appl. Math. 208 (2007), 280-301. (2007) MR2347750DOI10.1016/j.cam.2006.10.085
  4. Burenkov, V. I., Guliyev, H. V., Tararykova, T. V., Serbetci, A., 10.1134/S1064562408050025, Dokl. Math. 78 (2008), 651-654 Translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 422 (2008), 11-14. (2008) MR2475077DOI10.1134/S1064562408050025
  5. Burenkov, V. I., Guliyev, V. S., 10.1007/s11118-008-9113-5, Potential Anal. 30 (2009), 211-249. (2009) Zbl1171.42003MR2480959DOI10.1007/s11118-008-9113-5
  6. Burenkov, V. I., Gogatishvili, A., Guliyev, V. S., Mustafayev, R. Ch., Boundedness of the fractional maximal operator in Morrey-type spaces, Complex Var. Elliptic Equ. 55 (2010), 739-758. (2010) MR2674862
  7. Evans, W. D., Gogatishvili, A., Opic, B., The reverse Hardy inequality with measures, Math. Inequal. Appl. 11 (2008), 43-74. (2008) Zbl1136.26004MR2376257
  8. Gogatishvili, A., Mustafayev, R., The multidimensional reverse Hardy inequalities, Math. Inequal. & Appl. 14 (2011) (to appear) Preprint, Institute of Mathematics, AS CR, Prague 2009-5-27. Available at http://www.math.cas.cz/preprint/pre-179.pdf. MR2853078
  9. Guliyev, V. S., Integral operators on function spaces on the homogeneous groups and on domains in ℝ n , Doctor's degree dissertation Mat. Inst. Steklov Moscow (1994), Russian. (1994) 
  10. Guliyev, V. S., Function Spaces, Integral Operators and Two Weighted Inequalities on Homogeneous Groups. Some Applications, Baku (1999), Russian. (1999) 
  11. Guliyev, V. S., Mustafayev, R. Ch., Integral operators of potential type in spaces of homogeneous type, Dokl. Math. 55 (1997), 427-429 Translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 354 (1997), 730-732. (1997) MR1473130
  12. Guliyev, V. S., Mustafayev, R. Ch., Fractional integrals on spaces of homogeneous type, Anal. Math. 24 (1998), 1810-200 Russian. (1998) 

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